/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date:        15. February 2012
* $Revision: 	V1.1.0
*
* Project: 	    CMSIS DSP Library
* Title:	    arm_cfft_radix4_f32.c
*
* Description:	Radix-4 Decimation in Frequency CFFT & CIFFT Floating point processing function
*
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.1.0 2012/02/15
*    Updated with more optimizations, bug fixes and minor API changes.
*
* Version 1.0.10 2011/7/15
*    Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
*    Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
*    Documentation updated.
*
* Version 1.0.1 2010/10/05
*    Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
*    Production release and review comments incorporated.
*
* Version 0.0.5  2010/04/26
* 	 incorporated review comments and updated with latest CMSIS layer
*
* Version 0.0.3  2010/03/10
*    Initial version
* -------------------------------------------------------------------- */

#include "arm_math.h"

/**
 * @ingroup groupTransforms
 */

/**
 * @defgroup Radix4_CFFT_CIFFT Radix-4 Complex FFT Functions
 *
 * \par
 * Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT).
 * Computational complexity of CFFT reduces drastically when compared to DFT.
 * \par
 * This set of functions implements CFFT/CIFFT
 * for Q15, Q31, and floating-point data types.  The functions operates on in-place buffer which uses same buffer for input and output.
 * Complex input is stored in input buffer in an interleaved fashion.
 *
 * \par
 * The functions operate on blocks of input and output data and each call to the function processes
 * <code>2*fftLen</code> samples through the transform.  <code>pSrc</code>  points to In-place arrays containing <code>2*fftLen</code> values.
 * \par
 * The <code>pSrc</code> points to the array of in-place buffer of size <code>2*fftLen</code> and inputs and outputs are stored in an interleaved fashion as shown below.
 * <pre> {real[0], imag[0], real[1], imag[1],..} </pre>
 *
 * \par Lengths supported by the transform:
 * \par
 * Internally, the function utilize a radix-4 decimation in frequency(DIF) algorithm
 * and the size of the FFT supported are of the lengths [16, 64, 256, 1024].
 *
 *
 * \par Algorithm:
 *
 * <b>Complex Fast Fourier Transform:</b>
 * \par
 * Input real and imaginary data:
 * <pre>
 * x(n) = xa + j * ya
 * x(n+N/4 ) = xb + j * yb
 * x(n+N/2 ) = xc + j * yc
 * x(n+3N 4) = xd + j * yd
 * </pre>
 * where N is length of FFT
 * \par
 * Output real and imaginary data:
 * <pre>
 * X(4r) = xa'+ j * ya'
 * X(4r+1) = xb'+ j * yb'
 * X(4r+2) = xc'+ j * yc'
 * X(4r+3) = xd'+ j * yd'
 * </pre>
 * \par
 * Twiddle factors for radix-4 FFT:
 * <pre>
 * Wn = co1 + j * (- si1)
 * W2n = co2 + j * (- si2)
 * W3n = co3 + j * (- si3)
 * </pre>
 *
 * \par
 * \image html CFFT.gif "Radix-4 Decimation-in Frequency Complex Fast Fourier Transform"
 *
 * \par
 * Output from Radix-4 CFFT Results in Digit reversal order. Interchange middle two branches of every butterfly results in Bit reversed output.
 * \par
 * <b> Butterfly CFFT equations:</b>
 * <pre>
 * xa' = xa + xb + xc + xd
 * ya' = ya + yb + yc + yd
 * xc' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
 * yc' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
 * xb' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
 * yb' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)
 * xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)
 * yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)
 * </pre>
 *
 *
 * <b>Complex Inverse Fast Fourier Transform:</b>
 * \par
 * CIFFT uses same twiddle factor table as CFFT with modifications in the design equation as shown below.
 *
 * \par
 * <b> Modified Butterfly CIFFT equations:</b>
 * <pre>
 * xa' = xa + xb + xc + xd
 * ya' = ya + yb + yc + yd
 * xc' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)
 * yc' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)
 * xb' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)
 * yb' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2)
 * xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3)
 * yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3)
 * </pre>
 *
 * \par Instance Structure
 * A separate instance structure must be defined for each Instance but the twiddle factors and bit reversal tables can be reused.
 * There are separate instance structure declarations for each of the 3 supported data types.
 *
 * \par Initialization Functions
 * There is also an associated initialization function for each data type.
 * The initialization function performs the following operations:
 * - Sets the values of the internal structure fields.
 * - Initializes twiddle factor table and bit reversal table pointers
 * \par
 * Use of the initialization function is optional.
 * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
 * To place an instance structure into a const data section, the instance structure must be manually initialized.
 * Manually initialize the instance structure as follows:
 * <pre>
 *arm_cfft_radix4_instance_f32 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor, onebyfftLen};
 *arm_cfft_radix4_instance_q31 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};
 *arm_cfft_radix4_instance_q15 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};
 * </pre>
 * \par
 * where <code>fftLen</code> length of CFFT/CIFFT; <code>ifftFlag</code> Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT);
 * <code>bitReverseFlag</code> Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order);
 * <code>pTwiddle</code>points to array of twiddle coefficients; <code>pBitRevTable</code> points to the array of bit reversal table.
 * <code>twidCoefModifier</code> modifier for twiddle factor table which supports all FFT lengths with same table;
 * <code>pBitRevTable</code> modifier for bit reversal table which supports all FFT lengths with same table.
 * <code>onebyfftLen</code> value of 1/fftLen to calculate CIFFT;
 *
 * \par Fixed-Point Behavior
 * Care must be taken when using the fixed-point versions of the CFFT/CIFFT function.
 * Refer to the function specific documentation below for usage guidelines.
 */


/**
 * @addtogroup Radix4_CFFT_CIFFT
 * @{
 */

/**
 * @details
 * @brief Processing function for the floating-point Radix-4 CFFT/CIFFT.
 * @param[in]      *S    points to an instance of the floating-point Radix-4 CFFT/CIFFT structure.
 * @param[in, out] *pSrc points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.
 * @return none.
 */

void arm_cfft_radix4_f32(
    const arm_cfft_radix4_instance_f32* S,
    float32_t* pSrc)
{

	if(S->ifftFlag == 1u) {
		/*  Complex IFFT radix-4  */
		arm_radix4_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle,
		                                 S->twidCoefModifier, S->onebyfftLen);
	} else {
		/*  Complex FFT radix-4  */
		arm_radix4_butterfly_f32(pSrc, S->fftLen, S->pTwiddle,
		                         S->twidCoefModifier);
	}

	if(S->bitReverseFlag == 1u) {
		/*  Bit Reversal */
		arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
	}

}


/**
 * @} end of Radix4_CFFT_CIFFT group
 */


/* ----------------------------------------------------------------------
** Internal helper function used by the FFTs
** ------------------------------------------------------------------- */

/*
 * @brief  Core function for the floating-point CFFT butterfly process.
 * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.
 * @param[in]      fftLen           length of the FFT.
 * @param[in]      *pCoef           points to the twiddle coefficient buffer.
 * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
 * @return none.
 */

void arm_radix4_butterfly_f32(
    float32_t* pSrc,
    uint16_t fftLen,
    float32_t* pCoef,
    uint16_t twidCoefModifier)
{

	float32_t co1, co2, co3, si1, si2, si3;
	uint32_t ia1, ia2, ia3;
	uint32_t i0, i1, i2, i3;
	uint32_t n1, n2, j, k;

#ifndef ARM_MATH_CM0

	/* Run the below code for Cortex-M4 and Cortex-M3 */

	float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn;
	float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc,
	          Ybminusd;
	float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out;
	float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out;
	float32_t* ptr1;

	/*  Initializations for the first stage */
	n2 = fftLen;
	n1 = n2;

	/* n2 = fftLen/4 */
	n2 >>= 2u;
	i0 = 0u;
	ia1 = 0u;

	j = n2;

	/*  Calculation of first stage */
	do {
		/*  index calculation for the input as, */
		/*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
		i1 = i0 + n2;
		i2 = i1 + n2;
		i3 = i2 + n2;

		xaIn = pSrc[(2u * i0)];
		yaIn = pSrc[(2u * i0) + 1u];

		xcIn = pSrc[(2u * i2)];
		ycIn = pSrc[(2u * i2) + 1u];

		xbIn = pSrc[(2u * i1)];
		ybIn = pSrc[(2u * i1) + 1u];

		xdIn = pSrc[(2u * i3)];
		ydIn = pSrc[(2u * i3) + 1u];

		/* xa + xc */
		Xaplusc = xaIn + xcIn;
		/* xb + xd */
		Xbplusd = xbIn + xdIn;
		/* ya + yc */
		Yaplusc = yaIn + ycIn;
		/* yb + yd */
		Ybplusd = ybIn + ydIn;

		/*  index calculation for the coefficients */
		ia2 = ia1 + ia1;
		co2 = pCoef[ia2 * 2u];
		si2 = pCoef[(ia2 * 2u) + 1u];

		/* xa - xc */
		Xaminusc = xaIn - xcIn;
		/* xb - xd */
		Xbminusd = xbIn - xdIn;
		/* ya - yc */
		Yaminusc = yaIn - ycIn;
		/* yb + yd */
		Ybminusd = ybIn - ydIn;

		/* xa' = xa + xb + xc + xd */
		pSrc[(2u * i0)] = Xaplusc + Xbplusd;
		/* ya' = ya + yb + yc + yd */
		pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;

		/* (xa - xc) + (yb - yd) */
		Xb12C_out = (Xaminusc + Ybminusd);
		/* (ya - yc) + (xb - xd) */
		Yb12C_out = (Yaminusc - Xbminusd);
		/* (xa + xc) - (xb + xd) */
		Xc12C_out = (Xaplusc - Xbplusd);
		/* (ya + yc) - (yb + yd) */
		Yc12C_out = (Yaplusc - Ybplusd);
		/* (xa - xc) - (yb - yd) */
		Xd12C_out = (Xaminusc - Ybminusd);
		/* (ya - yc) + (xb - xd) */
		Yd12C_out = (Xbminusd + Yaminusc);

		co1 = pCoef[ia1 * 2u];
		si1 = pCoef[(ia1 * 2u) + 1u];

		/*  index calculation for the coefficients */
		ia3 = ia2 + ia1;
		co3 = pCoef[ia3 * 2u];
		si3 = pCoef[(ia3 * 2u) + 1u];

		Xb12_out = Xb12C_out * co1;
		Yb12_out = Yb12C_out * co1;
		Xc12_out = Xc12C_out * co2;
		Yc12_out = Yc12C_out * co2;
		Xd12_out = Xd12C_out * co3;
		Yd12_out = Yd12C_out * co3;

		/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
		Xb12_out += Yb12C_out * si1;
		/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
		Yb12_out -= Xb12C_out * si1;
		/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
		Xc12_out += Yc12C_out * si2;
		/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
		Yc12_out -= Xc12C_out * si2;
		/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
		Xd12_out += Yd12C_out * si3;
		/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
		Yd12_out -= Xd12C_out * si3;


		/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
		pSrc[2u * i1] = Xc12_out;

		/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
		pSrc[(2u * i1) + 1u] = Yc12_out;

		/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
		pSrc[2u * i2] = Xb12_out;

		/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
		pSrc[(2u * i2) + 1u] = Yb12_out;

		/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
		pSrc[2u * i3] = Xd12_out;

		/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
		pSrc[(2u * i3) + 1u] = Yd12_out;

		/*  Twiddle coefficients index modifier */
		ia1 = ia1 + twidCoefModifier;

		/*  Updating input index */
		i0 = i0 + 1u;

	} while(--j);

	twidCoefModifier <<= 2u;

	/*  Calculation of second stage to excluding last stage */
	for(k = fftLen / 4; k > 4u; k >>= 2u) {
		/*  Initializations for the first stage */
		n1 = n2;
		n2 >>= 2u;
		ia1 = 0u;

		/*  Calculation of first stage */
		for(j = 0u; j <= (n2 - 1u); j++) {
			/*  index calculation for the coefficients */
			ia2 = ia1 + ia1;
			ia3 = ia2 + ia1;
			co1 = pCoef[ia1 * 2u];
			si1 = pCoef[(ia1 * 2u) + 1u];
			co2 = pCoef[ia2 * 2u];
			si2 = pCoef[(ia2 * 2u) + 1u];
			co3 = pCoef[ia3 * 2u];
			si3 = pCoef[(ia3 * 2u) + 1u];

			/*  Twiddle coefficients index modifier */
			ia1 = ia1 + twidCoefModifier;

			for(i0 = j; i0 < fftLen; i0 += n1) {
				/*  index calculation for the input as, */
				/*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
				i1 = i0 + n2;
				i2 = i1 + n2;
				i3 = i2 + n2;

				xaIn = pSrc[(2u * i0)];
				yaIn = pSrc[(2u * i0) + 1u];

				xbIn = pSrc[(2u * i1)];
				ybIn = pSrc[(2u * i1) + 1u];

				xcIn = pSrc[(2u * i2)];
				ycIn = pSrc[(2u * i2) + 1u];

				xdIn = pSrc[(2u * i3)];
				ydIn = pSrc[(2u * i3) + 1u];

				/* xa - xc */
				Xaminusc = xaIn - xcIn;
				/* (xb - xd) */
				Xbminusd = xbIn - xdIn;
				/* ya - yc */
				Yaminusc = yaIn - ycIn;
				/* (yb - yd) */
				Ybminusd = ybIn - ydIn;

				/* xa + xc */
				Xaplusc = xaIn + xcIn;
				/* xb + xd */
				Xbplusd = xbIn + xdIn;
				/* ya + yc */
				Yaplusc = yaIn + ycIn;
				/* yb + yd */
				Ybplusd = ybIn + ydIn;

				/* (xa - xc) + (yb - yd) */
				Xb12C_out = (Xaminusc + Ybminusd);
				/* (ya - yc) -  (xb - xd) */
				Yb12C_out = (Yaminusc - Xbminusd);
				/* xa + xc -(xb + xd) */
				Xc12C_out = (Xaplusc - Xbplusd);
				/* (ya + yc) - (yb + yd) */
				Yc12C_out = (Yaplusc - Ybplusd);
				/* (xa - xc) - (yb - yd) */
				Xd12C_out = (Xaminusc - Ybminusd);
				/* (ya - yc) +  (xb - xd) */
				Yd12C_out = (Xbminusd + Yaminusc);

				pSrc[(2u * i0)] = Xaplusc + Xbplusd;
				pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;

				Xb12_out = Xb12C_out * co1;
				Yb12_out = Yb12C_out * co1;
				Xc12_out = Xc12C_out * co2;
				Yc12_out = Yc12C_out * co2;
				Xd12_out = Xd12C_out * co3;
				Yd12_out = Yd12C_out * co3;

				/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
				Xb12_out += Yb12C_out * si1;
				/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
				Yb12_out -= Xb12C_out * si1;
				/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
				Xc12_out += Yc12C_out * si2;
				/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
				Yc12_out -= Xc12C_out * si2;
				/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
				Xd12_out += Yd12C_out * si3;
				/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
				Yd12_out -= Xd12C_out * si3;

				/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
				pSrc[2u * i1] = Xc12_out;

				/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
				pSrc[(2u * i1) + 1u] = Yc12_out;

				/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
				pSrc[2u * i2] = Xb12_out;

				/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
				pSrc[(2u * i2) + 1u] = Yb12_out;

				/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
				pSrc[2u * i3] = Xd12_out;

				/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
				pSrc[(2u * i3) + 1u] = Yd12_out;

			}
		}

		twidCoefModifier <<= 2u;
	}

	j = fftLen >> 2;
	ptr1 = &pSrc[0];

	/*  Calculations of last stage */
	do {

		xaIn = ptr1[0];
		xcIn = ptr1[4];
		yaIn = ptr1[1];
		ycIn = ptr1[5];

		/* xa + xc */
		Xaplusc = xaIn + xcIn;

		xbIn = ptr1[2];

		/* xa - xc */
		Xaminusc = xaIn - xcIn;

		xdIn = ptr1[6];

		/* ya + yc */
		Yaplusc = yaIn + ycIn;

		ybIn = ptr1[3];

		/* ya - yc */
		Yaminusc = yaIn - ycIn;

		ydIn = ptr1[7];

		/* xb + xd */
		Xbplusd = xbIn + xdIn;

		/* yb + yd */
		Ybplusd = ybIn + ydIn;

		/* xa' = xa + xb + xc + xd */
		ptr1[0] = (Xaplusc + Xbplusd);

		/* (xb-xd) */
		Xbminusd = xbIn - xdIn;

		/* ya' = ya + yb + yc + yd */
		ptr1[1] = (Yaplusc + Ybplusd);

		/* (yb-yd) */
		Ybminusd = ybIn - ydIn;

		/* xc' = (xa-xb+xc-xd) */
		ptr1[2] = (Xaplusc - Xbplusd);
		/* yc' = (ya-yb+yc-yd) */
		ptr1[3] = (Yaplusc - Ybplusd);
		/* xb' = (xa+yb-xc-yd) */
		ptr1[4] = (Xaminusc + Ybminusd);
		/* yb' = (ya-xb-yc+xd) */
		ptr1[5] = (Yaminusc - Xbminusd);
		/* xd' = (xa-yb-xc+yd)) */
		ptr1[6] = (Xaminusc - Ybminusd);
		/* yd' = (ya+xb-yc-xd) */
		ptr1[7] = (Xbminusd + Yaminusc);

		/* increment pointer by 8 */
		ptr1 = ptr1 + 8u;

	} while(--j);

#else

	float32_t t1, t2, r1, r2, s1, s2;

	/* Run the below code for Cortex-M0 */

	/*  Initializations for the fft calculation */
	n2 = fftLen;
	n1 = n2;

	for(k = fftLen; k > 1u; k >>= 2u) {
		/*  Initializations for the fft calculation */
		n1 = n2;
		n2 >>= 2u;
		ia1 = 0u;

		/*  FFT Calculation */
		for(j = 0u; j <= (n2 - 1u); j++) {
			/*  index calculation for the coefficients */
			ia2 = ia1 + ia1;
			ia3 = ia2 + ia1;
			co1 = pCoef[ia1 * 2u];
			si1 = pCoef[(ia1 * 2u) + 1u];
			co2 = pCoef[ia2 * 2u];
			si2 = pCoef[(ia2 * 2u) + 1u];
			co3 = pCoef[ia3 * 2u];
			si3 = pCoef[(ia3 * 2u) + 1u];

			/*  Twiddle coefficients index modifier */
			ia1 = ia1 + twidCoefModifier;

			for(i0 = j; i0 < fftLen; i0 += n1) {
				/*  index calculation for the input as, */
				/*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
				i1 = i0 + n2;
				i2 = i1 + n2;
				i3 = i2 + n2;

				/* xa + xc */
				r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];

				/* xa - xc */
				r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];

				/* ya + yc */
				s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];

				/* ya - yc */
				s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

				/* xb + xd */
				t1 = pSrc[2u * i1] + pSrc[2u * i3];

				/* xa' = xa + xb + xc + xd */
				pSrc[2u * i0] = r1 + t1;

				/* xa + xc -(xb + xd) */
				r1 = r1 - t1;

				/* yb + yd */
				t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];

				/* ya' = ya + yb + yc + yd */
				pSrc[(2u * i0) + 1u] = s1 + t2;

				/* (ya + yc) - (yb + yd) */
				s1 = s1 - t2;

				/* (yb - yd) */
				t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];

				/* (xb - xd) */
				t2 = pSrc[2u * i1] - pSrc[2u * i3];

				/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
				pSrc[2u * i1] = (r1 * co2) + (s1 * si2);

				/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
				pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);

				/* (xa - xc) + (yb - yd) */
				r1 = r2 + t1;

				/* (xa - xc) - (yb - yd) */
				r2 = r2 - t1;

				/* (ya - yc) -  (xb - xd) */
				s1 = s2 - t2;

				/* (ya - yc) +  (xb - xd) */
				s2 = s2 + t2;

				/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
				pSrc[2u * i2] = (r1 * co1) + (s1 * si1);

				/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
				pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);

				/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
				pSrc[2u * i3] = (r2 * co3) + (s2 * si3);

				/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
				pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);
			}
		}

		twidCoefModifier <<= 2u;
	}

#endif /* #ifndef ARM_MATH_CM0 */

}

/*
 * @brief  Core function for the floating-point CIFFT butterfly process.
 * @param[in, out] *pSrc            points to the in-place buffer of floating-point data type.
 * @param[in]      fftLen           length of the FFT.
 * @param[in]      *pCoef           points to twiddle coefficient buffer.
 * @param[in]      twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
 * @param[in]      onebyfftLen      value of 1/fftLen.
 * @return none.
 */

void arm_radix4_butterfly_inverse_f32(
    float32_t* pSrc,
    uint16_t fftLen,
    float32_t* pCoef,
    uint16_t twidCoefModifier,
    float32_t onebyfftLen)
{
	float32_t co1, co2, co3, si1, si2, si3;
	uint32_t ia1, ia2, ia3;
	uint32_t i0, i1, i2, i3;
	uint32_t n1, n2, j, k;

#ifndef ARM_MATH_CM0

	float32_t xaIn, yaIn, xbIn, ybIn, xcIn, ycIn, xdIn, ydIn;
	float32_t Xaplusc, Xbplusd, Yaplusc, Ybplusd, Xaminusc, Xbminusd, Yaminusc,
	          Ybminusd;
	float32_t Xb12C_out, Yb12C_out, Xc12C_out, Yc12C_out, Xd12C_out, Yd12C_out;
	float32_t Xb12_out, Yb12_out, Xc12_out, Yc12_out, Xd12_out, Yd12_out;
	float32_t* ptr1;


	/*  Initializations for the first stage */
	n2 = fftLen;
	n1 = n2;

	/* n2 = fftLen/4 */
	n2 >>= 2u;
	i0 = 0u;
	ia1 = 0u;

	j = n2;

	/*  Calculation of first stage */
	do {
		/*  index calculation for the input as, */
		/*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
		i1 = i0 + n2;
		i2 = i1 + n2;
		i3 = i2 + n2;

		/*  Butterfly implementation */
		xaIn = pSrc[(2u * i0)];
		yaIn = pSrc[(2u * i0) + 1u];

		xcIn = pSrc[(2u * i2)];
		ycIn = pSrc[(2u * i2) + 1u];

		xbIn = pSrc[(2u * i1)];
		ybIn = pSrc[(2u * i1) + 1u];

		xdIn = pSrc[(2u * i3)];
		ydIn = pSrc[(2u * i3) + 1u];

		/* xa + xc */
		Xaplusc = xaIn + xcIn;
		/* xb + xd */
		Xbplusd = xbIn + xdIn;
		/* ya + yc */
		Yaplusc = yaIn + ycIn;
		/* yb + yd */
		Ybplusd = ybIn + ydIn;

		/*  index calculation for the coefficients */
		ia2 = ia1 + ia1;
		co2 = pCoef[ia2 * 2u];
		si2 = pCoef[(ia2 * 2u) + 1u];

		/* xa - xc */
		Xaminusc = xaIn - xcIn;
		/* xb - xd */
		Xbminusd = xbIn - xdIn;
		/* ya - yc */
		Yaminusc = yaIn - ycIn;
		/* yb - yd */
		Ybminusd = ybIn - ydIn;

		/* xa' = xa + xb + xc + xd */
		pSrc[(2u * i0)] = Xaplusc + Xbplusd;

		/* ya' = ya + yb + yc + yd */
		pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;

		/* (xa - xc) - (yb - yd) */
		Xb12C_out = (Xaminusc - Ybminusd);
		/* (ya - yc) + (xb - xd) */
		Yb12C_out = (Yaminusc + Xbminusd);
		/* (xa + xc) - (xb + xd) */
		Xc12C_out = (Xaplusc - Xbplusd);
		/* (ya + yc) - (yb + yd) */
		Yc12C_out = (Yaplusc - Ybplusd);
		/* (xa - xc) + (yb - yd) */
		Xd12C_out = (Xaminusc + Ybminusd);
		/* (ya - yc) - (xb - xd) */
		Yd12C_out = (Yaminusc - Xbminusd);

		co1 = pCoef[ia1 * 2u];
		si1 = pCoef[(ia1 * 2u) + 1u];

		/*  index calculation for the coefficients */
		ia3 = ia2 + ia1;
		co3 = pCoef[ia3 * 2u];
		si3 = pCoef[(ia3 * 2u) + 1u];

		Xb12_out = Xb12C_out * co1;
		Yb12_out = Yb12C_out * co1;
		Xc12_out = Xc12C_out * co2;
		Yc12_out = Yc12C_out * co2;
		Xd12_out = Xd12C_out * co3;
		Yd12_out = Yd12C_out * co3;

		/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
		Xb12_out -= Yb12C_out * si1;
		/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
		Yb12_out += Xb12C_out * si1;
		/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
		Xc12_out -= Yc12C_out * si2;
		/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
		Yc12_out += Xc12C_out * si2;
		/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
		Xd12_out -= Yd12C_out * si3;
		/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
		Yd12_out += Xd12C_out * si3;

		/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
		pSrc[2u * i1] = Xc12_out;

		/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
		pSrc[(2u * i1) + 1u] = Yc12_out;

		/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
		pSrc[2u * i2] = Xb12_out;

		/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
		pSrc[(2u * i2) + 1u] = Yb12_out;

		/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
		pSrc[2u * i3] = Xd12_out;

		/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
		pSrc[(2u * i3) + 1u] = Yd12_out;

		/*  Twiddle coefficients index modifier */
		ia1 = ia1 + twidCoefModifier;

		/*  Updating input index */
		i0 = i0 + 1u;

	} while(--j);

	twidCoefModifier <<= 2u;

	/*  Calculation of second stage to excluding last stage */
	for(k = fftLen / 4; k > 4u; k >>= 2u) {
		/*  Initializations for the first stage */
		n1 = n2;
		n2 >>= 2u;
		ia1 = 0u;

		/*  Calculation of first stage */
		for(j = 0u; j <= (n2 - 1u); j++) {
			/*  index calculation for the coefficients */
			ia2 = ia1 + ia1;
			ia3 = ia2 + ia1;
			co1 = pCoef[ia1 * 2u];
			si1 = pCoef[(ia1 * 2u) + 1u];
			co2 = pCoef[ia2 * 2u];
			si2 = pCoef[(ia2 * 2u) + 1u];
			co3 = pCoef[ia3 * 2u];
			si3 = pCoef[(ia3 * 2u) + 1u];

			/*  Twiddle coefficients index modifier */
			ia1 = ia1 + twidCoefModifier;

			for(i0 = j; i0 < fftLen; i0 += n1) {
				/*  index calculation for the input as, */
				/*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
				i1 = i0 + n2;
				i2 = i1 + n2;
				i3 = i2 + n2;

				xaIn = pSrc[(2u * i0)];
				yaIn = pSrc[(2u * i0) + 1u];

				xbIn = pSrc[(2u * i1)];
				ybIn = pSrc[(2u * i1) + 1u];

				xcIn = pSrc[(2u * i2)];
				ycIn = pSrc[(2u * i2) + 1u];

				xdIn = pSrc[(2u * i3)];
				ydIn = pSrc[(2u * i3) + 1u];

				/* xa - xc */
				Xaminusc = xaIn - xcIn;
				/* (xb - xd) */
				Xbminusd = xbIn - xdIn;
				/* ya - yc */
				Yaminusc = yaIn - ycIn;
				/* (yb - yd) */
				Ybminusd = ybIn - ydIn;

				/* xa + xc */
				Xaplusc = xaIn + xcIn;
				/* xb + xd */
				Xbplusd = xbIn + xdIn;
				/* ya + yc */
				Yaplusc = yaIn + ycIn;
				/* yb + yd */
				Ybplusd = ybIn + ydIn;

				/* (xa - xc) - (yb - yd) */
				Xb12C_out = (Xaminusc - Ybminusd);
				/* (ya - yc) +  (xb - xd) */
				Yb12C_out = (Yaminusc + Xbminusd);
				/* xa + xc -(xb + xd) */
				Xc12C_out = (Xaplusc - Xbplusd);
				/* (ya + yc) - (yb + yd) */
				Yc12C_out = (Yaplusc - Ybplusd);
				/* (xa - xc) + (yb - yd) */
				Xd12C_out = (Xaminusc + Ybminusd);
				/* (ya - yc) -  (xb - xd) */
				Yd12C_out = (Yaminusc - Xbminusd);

				pSrc[(2u * i0)] = Xaplusc + Xbplusd;
				pSrc[(2u * i0) + 1u] = Yaplusc + Ybplusd;

				Xb12_out = Xb12C_out * co1;
				Yb12_out = Yb12C_out * co1;
				Xc12_out = Xc12C_out * co2;
				Yc12_out = Yc12C_out * co2;
				Xd12_out = Xd12C_out * co3;
				Yd12_out = Yd12C_out * co3;

				/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
				Xb12_out -= Yb12C_out * si1;
				/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
				Yb12_out += Xb12C_out * si1;
				/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
				Xc12_out -= Yc12C_out * si2;
				/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
				Yc12_out += Xc12C_out * si2;
				/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
				Xd12_out -= Yd12C_out * si3;
				/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
				Yd12_out += Xd12C_out * si3;

				/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
				pSrc[2u * i1] = Xc12_out;

				/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
				pSrc[(2u * i1) + 1u] = Yc12_out;

				/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
				pSrc[2u * i2] = Xb12_out;

				/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
				pSrc[(2u * i2) + 1u] = Yb12_out;

				/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
				pSrc[2u * i3] = Xd12_out;

				/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
				pSrc[(2u * i3) + 1u] = Yd12_out;

			}
		}

		twidCoefModifier <<= 2u;
	}

	/*  Initializations of last stage */

	j = fftLen >> 2;
	ptr1 = &pSrc[0];

	/*  Calculations of last stage */
	do {

		xaIn = ptr1[0];
		xcIn = ptr1[4];
		yaIn = ptr1[1];
		ycIn = ptr1[5];

		/*  Butterfly implementation */
		/* xa + xc */
		Xaplusc = xaIn + xcIn;

		xbIn = ptr1[2];

		/* xa - xc */
		Xaminusc = xaIn - xcIn;

		xdIn = ptr1[6];

		/* ya + yc */
		Yaplusc = yaIn + ycIn;

		ybIn = ptr1[3];

		/* ya - yc */
		Yaminusc = yaIn - ycIn;

		ydIn = ptr1[7];

		/* xc + xd */
		Xbplusd = xbIn + xdIn;

		/* yb + yd */
		Ybplusd = ybIn + ydIn;

		/* xa' = xa + xb + xc + xd */
		ptr1[0] = (Xaplusc + Xbplusd) * onebyfftLen;

		/* (xb-xd) */
		Xbminusd = xbIn - xdIn;

		/* ya' = ya + yb + yc + yd */
		ptr1[1] = (Yaplusc + Ybplusd) * onebyfftLen;

		/* (yb-yd) */
		Ybminusd = ybIn - ydIn;

		/* xc' = (xa-xb+xc-xd) * onebyfftLen */
		ptr1[2] = (Xaplusc - Xbplusd) * onebyfftLen;

		/* yc' = (ya-yb+yc-yd) * onebyfftLen  */
		ptr1[3] = (Yaplusc - Ybplusd) * onebyfftLen;

		/* xb' = (xa-yb-xc+yd) * onebyfftLen */
		ptr1[4] = (Xaminusc - Ybminusd) * onebyfftLen;

		/* yb' = (ya+xb-yc-xd) * onebyfftLen */
		ptr1[5] = (Yaminusc + Xbminusd) * onebyfftLen;

		/* xd' = (xa-yb-xc+yd) * onebyfftLen */
		ptr1[6] = (Xaminusc + Ybminusd) * onebyfftLen;

		/* yd' = (ya-xb-yc+xd) * onebyfftLen */
		ptr1[7] = (Yaminusc - Xbminusd) * onebyfftLen;

		/* increment source pointer by 8 for next calculations */
		ptr1 = ptr1 + 8u;

	} while(--j);

#else

	float32_t t1, t2, r1, r2, s1, s2;

	/* Run the below code for Cortex-M0 */

	/*  Initializations for the first stage */
	n2 = fftLen;
	n1 = n2;

	/*  Calculation of first stage */
	for(k = fftLen; k > 4u; k >>= 2u) {
		/*  Initializations for the first stage */
		n1 = n2;
		n2 >>= 2u;
		ia1 = 0u;

		/*  Calculation of first stage */
		for(j = 0u; j <= (n2 - 1u); j++) {
			/*  index calculation for the coefficients */
			ia2 = ia1 + ia1;
			ia3 = ia2 + ia1;
			co1 = pCoef[ia1 * 2u];
			si1 = pCoef[(ia1 * 2u) + 1u];
			co2 = pCoef[ia2 * 2u];
			si2 = pCoef[(ia2 * 2u) + 1u];
			co3 = pCoef[ia3 * 2u];
			si3 = pCoef[(ia3 * 2u) + 1u];

			/*  Twiddle coefficients index modifier */
			ia1 = ia1 + twidCoefModifier;

			for(i0 = j; i0 < fftLen; i0 += n1) {
				/*  index calculation for the input as, */
				/*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
				i1 = i0 + n2;
				i2 = i1 + n2;
				i3 = i2 + n2;

				/* xa + xc */
				r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];

				/* xa - xc */
				r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];

				/* ya + yc */
				s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];

				/* ya - yc */
				s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

				/* xb + xd */
				t1 = pSrc[2u * i1] + pSrc[2u * i3];

				/* xa' = xa + xb + xc + xd */
				pSrc[2u * i0] = r1 + t1;

				/* xa + xc -(xb + xd) */
				r1 = r1 - t1;

				/* yb + yd */
				t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];

				/* ya' = ya + yb + yc + yd */
				pSrc[(2u * i0) + 1u] = s1 + t2;

				/* (ya + yc) - (yb + yd) */
				s1 = s1 - t2;

				/* (yb - yd) */
				t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];

				/* (xb - xd) */
				t2 = pSrc[2u * i1] - pSrc[2u * i3];

				/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
				pSrc[2u * i1] = (r1 * co2) - (s1 * si2);

				/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
				pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);

				/* (xa - xc) - (yb - yd) */
				r1 = r2 - t1;

				/* (xa - xc) + (yb - yd) */
				r2 = r2 + t1;

				/* (ya - yc) +  (xb - xd) */
				s1 = s2 + t2;

				/* (ya - yc) -  (xb - xd) */
				s2 = s2 - t2;

				/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
				pSrc[2u * i2] = (r1 * co1) - (s1 * si1);

				/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
				pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);

				/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
				pSrc[2u * i3] = (r2 * co3) - (s2 * si3);

				/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
				pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);
			}
		}

		twidCoefModifier <<= 2u;
	}

	/*  Initializations of last stage */
	n1 = n2;
	n2 >>= 2u;

	/*  Calculations of last stage */
	for(i0 = 0u; i0 <= (fftLen - n1); i0 += n1) {
		/*  index calculation for the input as, */
		/*  pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
		i1 = i0 + n2;
		i2 = i1 + n2;
		i3 = i2 + n2;

		/*  Butterfly implementation */
		/* xa + xc */
		r1 = pSrc[2u * i0] + pSrc[2u * i2];

		/* xa - xc */
		r2 = pSrc[2u * i0] - pSrc[2u * i2];

		/* ya + yc */
		s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];

		/* ya - yc */
		s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];

		/* xc + xd */
		t1 = pSrc[2u * i1] + pSrc[2u * i3];

		/* xa' = xa + xb + xc + xd */
		pSrc[2u * i0] = (r1 + t1) * onebyfftLen;

		/* (xa + xb) - (xc + xd) */
		r1 = r1 - t1;

		/* yb + yd */
		t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];

		/* ya' = ya + yb + yc + yd */
		pSrc[(2u * i0) + 1u] = (s1 + t2) * onebyfftLen;

		/* (ya + yc) - (yb + yd) */
		s1 = s1 - t2;

		/* (yb-yd) */
		t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];

		/* (xb-xd) */
		t2 = pSrc[2u * i1] - pSrc[2u * i3];

		/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
		pSrc[2u * i1] = r1 * onebyfftLen;

		/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
		pSrc[(2u * i1) + 1u] = s1 * onebyfftLen;


		/* (xa - xc) - (yb-yd) */
		r1 = r2 - t1;

		/* (xa - xc) + (yb-yd) */
		r2 = r2 + t1;

		/* (ya - yc) + (xb-xd) */
		s1 = s2 + t2;

		/* (ya - yc) - (xb-xd) */
		s2 = s2 - t2;

		/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
		pSrc[2u * i2] = r1 * onebyfftLen;

		/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
		pSrc[(2u * i2) + 1u] = s1 * onebyfftLen;

		/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
		pSrc[2u * i3] = r2 * onebyfftLen;

		/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
		pSrc[(2u * i3) + 1u] = s2 * onebyfftLen;
	}

#endif /* #ifndef ARM_MATH_CM0 */

}
